Problem: Multiply the following complex numbers, marked as blue dots on the graph: $( e^{\pi i / 4}) \cdot (7 e^{7\pi i / 12})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{\pi i / 4}$ ) has angle $\frac{1}{4}\pi$ and radius $1$ The second number ( $7 e^{7\pi i / 12}$ ) has angle $\frac{7}{12}\pi$ and radius $7$ The radius of the result will be $1 \cdot 7$ , which is $7$ The angle of the result is $\frac{1}{4}\pi + \frac{7}{12}\pi = \frac{5}{6}\pi$ The radius of the result is $7$ and the angle of the result is $\frac{5}{6}\pi$.